The v1.0.0-rc.1 spec says, regarding multi-line strings:

When the last non-whitespace character on a line is a \, it will be trimmed along with all whitespace (including newlines) up to the next non-whitespace character or closing delimiter. All of the escape sequences that are valid for basic strings are also valid for multi-line basic strings.

This is unclear for the case when that last \ is escaped. I think the ABNF is correct and when I tested with tomlkit it looks good:

>>> from tomlkit import parse
>>> parse(r'''
... ml-escaped-nl = """
...   foo \ 
...   bar \\ 
...   baz \\\ 
...   quux"""''')
{'ml-escaped-nl': '  foo bar \\ \n  baz \\quux'}

But I think the description in the spec can be clearer. I propose the following 1-word change (or 2 if you include the epenthesis of the preceding "a" to "an"):

- ending backslash". When the last non-whitespace character on a line is a `\`, it
+ ending backslash". When the last non-whitespace character on a line is an unescaped `\`, it 

The code snippet above might also be a good test case.

Aside: Is https://github.com/BurntSushi/toml-test the de jure, or even de facto, test set? It hasn't been updated in a while.